Question:
If $\sinh x = \frac{3}{4}$, then $\cosh 2x =$
If $\sinh x = \frac{3}{4}$, then $\cosh 2x =$
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Hyperbolic trigonometric identities are very similar to standard ones but watch out for sign differences ($\cosh^2 x - \sinh^2 x = 1$ and $\cosh 2x = 1 + 2\sinh^2 x$).
Updated On: May 31, 2026
- $\frac{17}{8}$
- $\frac{15}{8}$
- $\frac{9}{8}$
- $\frac{25}{8}$
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The Correct Option is A
Solution and Explanation
Step 1: Concept
We use the hyperbolic double-angle identity: $\cosh 2x = 1 + 2 \sinh^2 x$.
Step 2: Meaning
We are given $\sinh x = \frac{3}{4}$ and need to compute the value of $\cosh 2x$.
Step 3: Analysis
Substitute $\sinh x = \frac{3}{4}$ into the identity: \[ \cosh 2x = 1 + 2 \left(\frac{3}{4}\right)^2 = 1 + 2 \left(\frac{9}{16}\right) \] Simplify the expression: \[ \cosh 2x = 1 + \frac{9}{8} = \frac{17}{8} \]
Step 4: Conclusion
The value of $\cosh 2x$ is $\frac{17}{8}$. Final Answer: (A)
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